Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java.util.*;
public class Main {
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        boolean t=false;
        for (int i=1;i<n;i++){
            int x= i*(i+1)/2;
            int k = (int)(Math.sqrt((n-x)*2));
            if (k == 0)
            {
                t=false;
                break;
            }
            if (x+ k*(k+1)/2== n)
            {
                t=true;
                break;
            }
        }
        if(t==false) {
            System.out.println("NO");
        }else{
            System.out.println("YES");
        }
    }
}